Final Portafolios Rivera

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Abril 2012

GESTIN DE PORTAFOLIOS

Y PLANIFICACIN DE

INVERSIONESFINAL PROJECT: Testing the empirical implications

of an asset pricing model

INTEGRANTES:

Llanos Palomino, Ivo

Rivera Montoya, Marcos

Snchez Neyra, Jorge


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1. Project objective and some highlightsThis paper analyzes the behavior of the main six Peruvian stock market index sectors andempirically tries the validity of the CAPM model. It also analyzes the behavior of the variousindices of sectors listed on the BVL considering monthly data from 1999M01 to 2011M12.

E-Views regressions are listed below on annexes, showing also monthly statistical significance andstandard errors of the estimates.

1.1 Statistical description of the variables

1.2 Portfolio value over the time

0

1,000

2,000

3,000

4,000

5,000

6,000

IGBVL

Agriculture

Banks_Finance

Diverse

Industrial

MiningService


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1.3 Monthly variation (as a % growth rate) of sectors, copper and T-bill (1999M01-2011M12)

1.4 Correlation between BVL and Copper index price

Because mining companies represent a significant percentage of the Peruvian stock marketcapitalization we would be expected that IGBVL performance is strongly correlated with theprice of copper. Reviewing the historical correlation we observe that reaches a value of 0.54,although this reflects a positive correlation, surprises their low value, showing that there is a lowcorrelation between the performance of the Lima Stock Exchange and the price of copper.However, one must consider the context of the sample period, as in other periods their valuesalso changes considerably.

-60

-40

-20

0

20

40

60

80

100

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Agriculture

-30

-20

-10

0

10

20

30

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Bank_Financial

-40

-30

-20

-10

0

10

20

30

40

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Copper

-40

-30

-20

-10

0

10

20

30

40

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Diverse

-40

-30

-20

-10

0

10

20

30

40

50

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

IGBVL

-40

-30

-20

-10

0

10

20

30

40

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Industrial

-60

-40

-20

0

20

40

60

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Minig

-30

-20

-10

0

10

20

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

Services

.0

.1

.2

.3

.4

.5

.6

9 9 0 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 1 1

TBILL

-40

-30

-20

-10

0

10

20

30

40

50

99 00 01 02 03 04 05 06 07 08 09 10 11

Copper IGBVL


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1.5 Correlation matrix of the variables

2. Comments about main indicators Highests betas: sectors AGR and MIN with 1.223 and 1.167 respectively. Meanwhile the

lowest beta corresponds to SERVICE sector with 0.446 As we can expect, sector INDUSTRIAL exhibits the closest return on market with a 0.874

beta. When we regress with LME Copper we can observed that R2 and other statistical

indicators reduce it significance.


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Once obtained the betas for all sectors we proceed to compare the performance of theCAPM model for the Peruvian market. The CAPM model allows us to predict theperformance of an asset using variables such as risk-free rate (Rf), the excess marketreturn (Exc) and the beta of an asset.

With the data of sectorial betas we perform a cross-section regression between theaverage excess return of the sectors and the estimated betas in order to determine if thevalue of the regression coefficient is statistically different from the historical averageexcess market return. Performing a Wald test we found that the coefficient isstatistically different from the excess market return average, so we can conclude thatCAPM model does not predict correctly (or at least in a relevant way) the behavior of thePeruvian market.

Results below:


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The IGBVL has greater explanatory power than COPPER3M because the copper was not asvolatile during the period of the financial crisis; due in part to developing countriesdemand for copper that remained strong, which were not directly affected by this crisis.On the other hand, IGBVL does react strongly basically for bad US economic news, so thiscan be considered as a differentiating factor between the IGBVL and the price of copper.

The hypothesis of the CAPM performance in the Peruvian market cannot be rejected,because the regression coefficient of cross-sectorial betas explaining the sectorialaverage excess return is not significantly different from 2.02, the average excess returnof the market.

Because mining companies represent a significant percentage of the Peruvian stockmarket capitalization, one would expect IGBVL performance is strongly correlated withthe price of copper. Reviewing the historical correlation it reaches a value of 0.54,although this reflects a positive correlation, its low value, gives us a hint that there is alow correlation between the performance of the IGBVL and the price of copper.However, consider the context of the sample period: while IGBVL behavior and copperprices show a similar trend in levels, differences occur when both variables are observedwhen the trend is extracted, for example by taking the monthly variations.

Figure of point 1.4 shows more volatile IGBVL especially between 2008 and 2009 periodwhen the financial crisis breaks out in the U.S. So in the second half of 2008 the IGBVLregistered sharp falls, higher than those registered in the price of copper, for example inJuly fell 12.7% IGBV while copper did in 5.3%.

By 2009 the market settle down with the various rescue packages globally to prevent thefinancial crisis to collapse the major world economies, thus the price of copper and

therefore the IGBVL be recovered, but once again is the IGBVL which exhibits thegreatest volatility, recovering much faster than copper. Thus, for example, in March ofthat year the General Index registered a jump of 41.9%, while copper rises by 17.7%.


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Test de Wald:

We also performed Wald test in order to determine if specific risk could affect the cross/sectionof average sector excess returns. In this case, we will test the null hypothesis of the independentterm = 0. The systemic risk is represented by betas and the specific risk by the constant term.


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ANNEXES: Regression of sectorial variables

With IGBVL-TBILL excess return:


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With COPPER3M-TBILL excess return:

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Final Portafolios Rivera